On a stochastic wave equation in two space dimension: regularity of the solution and its density
Millet, Annie ; Morien, Pierre-Luc
HAL, hal-00258033 / Harvested from HAL
Text on HAL
We pursue the investigation started in a recent paper by Millet and Sanz-Solé concerning a non-linear wave equation driven by a Gaussian white noise in time and correlated in the two-dimensional space variable. Under more restrictive conditions on the covariance function of the noise, we prove Hölder-regularity properties for both the solution and its density. For the latter, we adapt the method used in a paper by Morien based on the Malliavin calculus.
Publié le : 2000-03-05
Classification:  Stochastic partial differential equation,  Wave equation,  Gaussian noise,  Malliavin calculus,  60H15 60H07,  [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] 
@article{hal-00258033,
     author = {Millet, Annie and Morien, Pierre-Luc},
     title = {On a stochastic wave equation in two space dimension: regularity of the solution and its density},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00258033}
}

Millet, Annie; Morien, Pierre-Luc. On a stochastic wave equation in two space dimension: regularity of the solution and its density. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00258033/